We have studied experimentally with high spatial and temporal resolution propagation of intense spin waves in microscopic Permalloy stripes. We show that the nonlinearity of the spin system of metallic magnetic films together with microscopic-scale confinement effects lead to an anomalous nonlinear magnetic dynamics, such as a nonlinear spatial self-modulation of spin waves characterized by the repulsive nonlinearity. This phenomenon appears to be densely connected with the nonlinear damping in the system. We find that both of these effects develop synchronously on the nanosecond temporal scale.